Given below are the four cases in which certain heat transfer is taking place:

1. Ice is melting in a glass full of water

2. Water is boiling in an open container

3. A metal rod is heated in a furnace

4. A cup of coffee is allowed to cool on a table

In which of the above cases, the Newton's Law of Cooling is applicable ?

CONCEPT:

Newton's Law of Cooling

EXPLANATION:

Newton's Law of Cooling states that the rate of change of temperature of an object is directly proportional to the difference in temperature between the object and its surroundings. This law is typically applicable to situations where an object is cooling or heating in the presence of a temperature difference with its environment.

1. Ice is melting in a glass full of water:
   • The melting of ice is more related to phase change and the absorption of latent heat rather than simple cooling or heating, and thus Newton's Law of Cooling is not directly applicable.
2. Water is boiling in an open container:
   • The boiling of water involves phase change and vaporization, which includes the absorption of latent heat and is not merely a simple cooling or heating process. Thus, Newton's Law of Cooling is not directly applicable.
3. A metal rod is heated in a furnace:
   • While heating in a furnace involves heat transfer, it is typically conducted at high temperatures and might involve various heat transfer mechanisms beyond simple cooling or heating to room temperature. Thus, Newton's Law of Cooling is not typically applicable here.
4. A cup of coffee is allowed to cool on a table:
   • This situation is a classic example of Newton's Law of Cooling, where the coffee cools by transferring heat to the surrounding air. The rate of cooling is proportional to the temperature difference between the coffee and the surroundings.

Therefore, the case where Newton's Law of Cooling is applicable is: (2) 4 only.